QuestionWrite the slope-intercept form of the equation of each line. 5) $x+3 y=-6$ 6) $x-7 y=-14$

Studdy Solution

STEP 1

What is this asking? We need to rewrite these equations, which are currently in standard form, into slope-intercept form, which looks like $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept. Watch out! Don't forget to completely isolate $y$ and be careful with those negative signs when moving terms around!

STEP 2

1. Solve for y in the first equation
2. Solve for y in the second equation

STEP 3

Alright, let's start with our first equation: $x + 3y = -6$ .
Our goal is to get $y$ all by itself.
It's like $y$ is at a party, and we want it to have some alone time!

STEP 4

First, let's move that $x$ to the other side of the equation.
Since it's being added on the left side, we'll subtract $x$ from both sides to keep things balanced.
This gives us $3y = -x - 6$ .
See how the $x$ hopped over and changed its sign?

STEP 5

Now, $y$ is almost alone, but it's still hanging out with that $3$ .
They're being multiplied, so to separate them, we'll divide both sides of the equation by $3$ .
This gives us $\frac{3y}{3} = \frac{-x - 6}{3}$ .

STEP 6

Let's simplify!
On the left side, the $3$ s divide to one, leaving us with just $y$ .
Awesome! On the right side, we can split the fraction to get $y = \frac{-x}{3} - \frac{6}{3}$ .

STEP 7

We can simplify that fraction with the $6$ to get $y = \frac{-1}{3}x - 2$ .
And there we have it!
Our first equation is now in slope-intercept form!

STEP 8

Okay, time for round two!
Our second equation is $x - 7y = -14$ .
Same goal: get $y$ by itself.

STEP 9

First, let's move that $x$ to the other side.
Since it's positive on the left, we'll subtract $x$ from both sides: $-7y = -x - 14$ .

STEP 10

Now, we need to detach that $-7$ from $y$ .
Since they're being multiplied, we'll divide both sides by $-7$ : $\frac{-7y}{-7} = \frac{-x - 14}{-7}$ .

STEP 11

Let's simplify!
On the left, the $-7$ s divide to one, leaving us with $y$ .
On the right, we can split the fraction and simplify the signs: $y = \frac{-x}{-7} - \frac{14}{-7}$ which becomes $y = \frac{1}{7}x + 2$ .

STEP 12

Boom! Our second equation is now also in slope-intercept form!

STEP 13

For equation 5) $x + 3y = -6$ , the slope-intercept form is $y = \frac{-1}{3}x - 2$ .
For equation 6) $x - 7y = -14$ , the slope-intercept form is $y = \frac{1}{7}x + 2$ .

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